Basics

An antenna is a transducer that converts guided electromagnetic waves (in a transmission line or waveguide) into free-space electromagnetic waves, and vice versa. It serves as the interface between the transmitter/receiver circuit and free space. Key functions include radiation (TX), reception (RX), and spatial filtering (directional selectivity).

As frequency increases, λ decreases, and the free-space path loss increases (the received power decreases for the same distance, assuming constant-gain antennas). The loss increases by 6dB every time frequency doubles or distance doubles.

• Directivity: The ratio of radiation intensity in a given direction to the average radiation intensity over all directions. A measure of how “focused” the pattern is.
• Radiation Efficiency (η): The ratio of radiated power to total input power, accounting for ohmic and dielectric losses.
• Gain: Directivity multiplied by radiation efficiency.

Gain is always ≤ Directivity. For a lossless antenna, Gain = Directivity.

• TRP (Total Radiated Power): The total power radiated in all directions, obtained by integrating the radiation pattern over the full sphere.
• EIRP (Effective Isotropic Radiated Power): The power an isotropic antenna would need to produce the same peak field strength. EIRP = P_input × G_peak.

EIRP is always ≥ TRP. For an isotropic antenna, EIRP = TRP. For a directional antenna, EIRP > TRP because gain concentrates energy in one direction.

The space around an antenna is divided into three regions:

• Reactive near-field: R < 0.62√(D³/λ). Energy is stored and returned to the antenna — E and H fields are not in phase and don't radiate. Impedance varies rapidly with distance.
• Radiating near-field (Fresnel): 0.62√(D³/λ) < R < 2D²/λ. Fields begin to radiate but the pattern depends on distance.
• Far-field (Fraunhofer): R > 2D²/λ. The radiation pattern is independent of distance, E and H fields are orthogonal and in phase, and power decays as 1/R².

where D is the largest antenna dimension.

Antenna impedance (Z_ant = R_ant + jX_ant) consists of:

• Radiation resistance (R_rad): Represents power actually radiated into space.
• Loss resistance (R_loss): Represents ohmic/dielectric losses dissipated as heat.
• Reactance (X_ant): Stored energy in the near field.

Matching the antenna impedance to the feed line (typically 50Ω) ensures maximum power transfer and minimizes reflections. A mismatch causes VSWR > 1, reducing radiated power and potentially damaging the transmitter.

Common benchmarks: VSWR 2:1 = |Γ| = 0.33 = Return Loss 9.5dB = 11% power reflected. VSWR 1.5:1 = RL 14dB = 4% reflected. A well-matched antenna typically has VSWR < 2:1 across its operating band.

Antenna bandwidth is the frequency range over which the antenna meets a specified performance criterion (typically VSWR < 2:1 or S11 < −10dB). Bandwidth is determined by:

• Antenna Q-factor: Lower Q = wider bandwidth. Q is inversely related to the antenna’s electrical volume.
• Chu-Harrington limit: Sets a fundamental lower bound on Q for a given antenna size — smaller antennas have higher Q and narrower bandwidth.
• Matching network: Can trade gain flatness for bandwidth.
• Antenna geometry: Thicker dipoles, wider slots, and tapered structures have lower Q and wider bandwidth.

• Main lobe: Direction of maximum radiation and its beamwidth (HPBW — half-power beamwidth).
• Side lobes: Undesired radiation in other directions, characterized by side-lobe level (SLL) in dB below the main lobe.
• Back lobe: Radiation in the direction opposite the main lobe. Front-to-back ratio (F/B) quantifies this.
• Nulls: Directions of zero (or minimum) radiation.
• Polarization: The orientation of the E-field vector (linear, circular, or elliptical).
• Beamwidth: HPBW (−3dB points) and FNBW (first-null beamwidth).

HPBW is the angular width between the two directions where the radiation intensity drops to half (−3dB) of its peak value. It is important because:

• It defines the angular resolution of the antenna — the ability to distinguish between two closely spaced targets (radar) or users (communications).
• Narrower HPBW = higher directivity = more focused beam.
• It determines the coverage area in base station antenna design.

For a uniformly illuminated aperture: HPBW ≈ 51λ/D (degrees), where D is the aperture dimension.

Polarization describes the orientation of the E-field vector as the wave propagates:

• Linear: E-field oscillates in a single plane (horizontal or vertical). Simple, but orientation must match between TX and RX antennas.
• Circular: E-field rotates in a circle (RHCP or LHCP). Created when two orthogonal linear components have equal amplitude and 90° phase difference. Eliminates polarization mismatch for any linear receive antenna (with 3dB loss).
• Elliptical: General case — E-field traces an ellipse. Occurs when the two orthogonal components have unequal amplitudes or non-90° phase difference.

Axial ratio (AR) characterizes polarization purity: AR = 1 (0dB) for perfect circular, AR = ∞ for linear. Typically, AR < 3dB is considered circular.

When transmit and receive antennas have different polarizations, not all power is captured. The polarization loss factor (PLF) is:

Examples:

• Matched polarizations (both vertical): PLF = 1 (0dB loss)
• Cross-polarized (vertical TX, horizontal RX): PLF = 0 (infinite loss — no power received)
• Circular TX to linear RX: PLF = 0.5 (−3dB loss)
• RHCP TX to LHCP RX: PLF = 0 (no power received — opposite sense CP)

The effective aperture (A_e) is the “capture area” of the antenna for incoming radiation:

Or equivalently: A_e = Gλ²/(4π). For an aperture antenna (dish, horn) with physical area A_phys and aperture efficiency η_ap:

Typical aperture efficiencies range from 50–70%. This equation shows why gain increases with frequency (for a fixed physical aperture) and why larger antennas have higher gain.

• Half-wave dipole: Two λ/4 arms, omnidirectional in the H-plane, gain ≈ 2.15dBi, impedance ≈ 73Ω. Balanced feed required.
• Quarter-wave monopole: Single λ/4 element over a ground plane. Behaves like half a dipole — omnidirectional, gain ≈ 5.15dBi (with infinite ground plane), impedance ≈ 36.5Ω. Unbalanced feed.
• Loop antenna: Small loops (circumference << λ) have very low radiation resistance and are used mainly for receive/direction finding. Full-wave loops (circumference ≈ λ) have gain comparable to a dipole with different pattern shape.

A patch antenna is a flat metallic element on a grounded dielectric substrate. The dominant mode creates a resonant cavity between the patch and ground plane.

Advantages: Low profile, lightweight, conformal to surfaces, easy to fabricate on PCBs, easily integrated with RF circuits, supports dual polarization.

Limitations: Narrow bandwidth (typically 1–5%, can be improved with thick substrates or stacked patches), low gain (5–8dBi for a single element), relatively high ohmic losses, and sensitivity to manufacturing tolerances.

Resonant length is approximately λ/2 in the dielectric (L ≈ λ₀/(2√ε_eff)).

A horn antenna is a flared waveguide that provides a gradual transition from the waveguide impedance to free-space impedance. Types include pyramidal, conical, and corrugated horns.

Key properties: Moderate to high gain (10–25dBi), wide bandwidth (can be >2:1), well-characterized and predictable radiation patterns, low VSWR.

Common uses: Gain reference standards for antenna measurements, feed elements for parabolic reflectors, EMC testing, and radar applications. Horn antennas are the “gold standard” calibration antenna because their gain can be accurately calculated from physical dimensions.

• Driven element: The only element connected to the feed (typically a half-wave dipole). Resonant at the operating frequency.
• Reflector: Placed behind the driven element, slightly longer than λ/2. It reflects energy forward, improving the front-to-back ratio.
• Directors: Placed in front, slightly shorter than λ/2. Each director focuses the beam further, increasing gain and narrowing the beamwidth.

More directors = higher gain, but with diminishing returns and narrower bandwidth. A typical 3-element Yagi has ~8dBi gain; a 10-element design can reach ~13dBi.

A slot antenna is a narrow rectangular opening cut in a conducting surface. By Babinet’s principle, a slot antenna is the electromagnetic complement of a dipole antenna:

• The E and H field patterns are swapped (E-plane ↔ H-plane).
• The polarization is rotated 90°.
• The impedances are related by: Z_slot × Z_dipole = η²/4, where η ≈ 377Ω.

For a half-wave slot: Z_slot = 377²/(4 × 73) ≈ 487Ω. Slot antennas are commonly used in aircraft (flush-mounted), waveguide arrays, and as cavity-backed elements.

A Planar Inverted-F Antenna (PIFA) is a patch antenna with a shorting pin/wall connecting the radiating element to the ground plane. This folding and shorting reduces the resonant length to approximately λ/4 instead of λ/2.

Why popular in mobile devices:

• Compact size — approximately half the size of a standard patch.
• Low profile — can be integrated inside device housings.
• Reduced ground-plane currents — lower SAR (Specific Absorption Rate) compared to external antennas.
• Moderate bandwidth — can be improved with parasitic elements or slots.
• Multiband capability — by adding slots, branches, or parasitic elements.

The array factor (AF) describes the radiation pattern contribution from the array geometry and phasing, independent of the individual element pattern. The total pattern is:

Element spacing effects (for a linear array):

• d < λ/2: No grating lobes, but reduced directivity and potential mutual coupling issues.
• d = λ/2: Optimal — maximum grating-lobe-free scan range, good directivity.
• d > λ/2: Grating lobes appear — additional main beams in undesired directions that waste power and cause interference.

Grating lobes are additional maxima in the array pattern that appear when element spacing is too large relative to wavelength. They are the spatial equivalent of aliasing. For a beam scanned to angle θ₀, the condition for no grating lobes is:

For broadside (θ₀ = 0°): d < λ. For full hemisphere scanning (θ₀ = 90°): d < λ/2. In practice, d ≈ 0.5λ is the standard choice for phased arrays to avoid grating lobes across all scan angles.

• Analog beamforming: Phase shifters adjust the phase of each element’s signal in the analog domain before combining. Only one beam direction at a time. Simple, lower power, but limited flexibility. Used in 5G mmWave.
• Digital beamforming: Each element has its own ADC/DAC. Beamforming is done digitally, allowing multiple simultaneous beams, adaptive nulling, and full MIMO capability. More flexible but requires more hardware and power.
• Hybrid beamforming: Combines both — analog subarrays with digital processing between subarrays. A practical compromise used in 5G massive MIMO.

Mutual coupling is the electromagnetic interaction between antenna elements in an array. When one element radiates, it induces currents in neighboring elements, affecting:

• Input impedance: Each element’s impedance changes depending on the excitation of its neighbors (active impedance ≠ isolated impedance).
• Radiation pattern: Element patterns are distorted, affecting the array pattern.
• Scan blindness: At certain scan angles, mutual coupling can cause a surface wave resonance that makes the array impedance extremely mismatched.
• Efficiency: Power absorbed by neighboring elements is not radiated from the intended element.

Mitigation: proper element spacing, decoupling networks, electromagnetic bandgap (EBG) structures, or defected ground planes between elements.

MIMO (Multiple-Input Multiple-Output) uses multiple antennas at both TX and RX to create independent spatial channels in a multipath environment.

• Beamforming: All antennas work together coherently to form a single, steered beam — increases SNR but transmits one data stream.
• Spatial multiplexing (MIMO): Each antenna transmits a different data stream simultaneously on the same frequency — increases throughput by a factor up to min(N_TX, N_RX).
• Diversity: Same data sent from multiple antennas with different coding — improves reliability in fading channels.

MIMO requires low correlation between antenna elements (sufficient spacing, different polarizations, or rich multipath).

Common measurement environments:

• Far-field outdoor range: Antenna under test (AUT) is placed at far-field distance from a source antenna. Simple but requires long distances and is affected by ground reflections and weather.
• Anechoic chamber: Indoor room lined with RF absorbers to simulate free-space. Compact, repeatable, weather-independent. Limited by chamber size at lower frequencies.
• Compact range: Uses a parabolic reflector to create a planar wave front at a shorter distance, effectively simulating far-field conditions indoors.
• Near-field scanning: Measures amplitude and phase on a surface close to the AUT (planar, cylindrical, or spherical scan), then mathematically transforms to the far-field pattern. Excellent for large antennas.

The gain-transfer (gain-comparison) method measures the AUT’s gain relative to a reference antenna with known gain (typically a standard-gain horn):

1. Measure received power with the reference antenna: P_ref
2. Replace with the AUT and measure received power: P_AUT
3. Calculate: G_AUT = G_ref + (P_AUT − P_ref) dB

This is the most common and practical method. The reference antenna’s gain must be accurately calibrated (traceable to national standards).

OTA testing measures the complete radiated performance of a wireless device (antenna + radio integrated together) rather than just the conducted RF performance or the antenna alone.

Key OTA metrics: TRP, TIS (Total Isotropic Sensitivity), EIS (Effective Isotropic Sensitivity), and EIRP. These capture real-world performance including body effects, chassis coupling, and component interactions.

Why important: Modern devices have integrated antennas that can’t be measured at a connector. The antenna performance is inseparable from the device design. Regulatory bodies and carriers (CTIA, 3GPP) require OTA testing for device certification.

In free space, Maxwell’s equations show that time-varying electric fields create magnetic fields and vice versa, enabling self-sustaining TEM wave propagation in any direction at the speed of light.

In a waveguide, conducting boundary conditions constrain the fields. Only specific field configurations (modes: TE, TM) can propagate, each with a cutoff frequency below which propagation is not supported. The waveguide acts as a high-pass filter, and the phase velocity is always greater than c while the group velocity is less than c.

• Free-space (LOS): Direct path, follows Friis equation. Dominates at microwave/mmWave frequencies with clear line of sight.
• Reflection: Wave bounces off surfaces larger than λ (buildings, ground). Governed by Snell’s law and Fresnel coefficients.
• Diffraction: Wave bends around obstacles comparable to λ (edges of buildings, hills). Explained by Huygens’ principle.
• Scattering: Wave interacts with objects smaller than or comparable to λ (foliage, rough surfaces, rain).
• Refraction: Wave bends when passing through media with different permittivity (atmospheric layers).
• Ground wave: Surface wave at LF/MF frequencies that follows Earth’s curvature.
• Ionospheric (sky wave): HF signals reflected by ionospheric layers for long-distance communication.

Multipath fading occurs when a signal reaches the receiver via multiple paths (direct, reflected, diffracted), each with different amplitude, phase, and delay. The signals combine constructively or destructively:

• Flat fading: All frequency components affected equally (delay spread << symbol period). Causes random amplitude variations.
• Frequency-selective fading: Different frequencies fade differently (delay spread ≈ symbol period). Causes ISI.
• Rayleigh fading: No dominant LOS path — amplitude follows Rayleigh distribution. Deep fades of 20–30dB are common.
• Rician fading: Dominant LOS path present — less severe fading.

Mitigation: diversity (spatial, polarization, frequency), equalization, OFDM, and MIMO.

At higher frequencies, the skin effect causes current to concentrate near the conductor surface. The skin depth:

decreases with frequency, reducing the effective cross-sectional area for current flow. This increases AC resistance and ohmic losses. At microwave frequencies, the skin depth in copper is only a few micrometers, meaning surface roughness and plating quality significantly impact performance.

The dielectric constant (ε_r) affects signal velocity: v = c/√ε_r. Higher ε_r means slower propagation and shorter wavelengths.

The loss tangent (tanδ) determines dielectric losses — higher tanδ means more signal attenuation, especially at higher frequencies. This is why low-loss materials (Rogers, Megtron) are used for RF boards instead of standard FR-4.

The Chu-Harrington limit is a fundamental bound on the minimum radiation Q-factor of an antenna based on the size of the smallest sphere that encloses it:

This means smaller antennas have inherently narrower bandwidth. No amount of clever design can overcome this physics limit. It’s critical for mobile device antenna design where space is constrained — it tells you the theoretical maximum bandwidth achievable for a given antenna volume.

Techniques for achieving multi-band operation:

• Multiple resonant paths: Branches or slots in the antenna structure create independent resonances at different frequencies.
• Parasitic elements: Additional coupled elements add resonances near the primary resonance, widening or adding bands.
• Tunable matching: Switch or varactor-tuned matching networks that reconfigure for different bands.
• Aperture tuning: Switches or varactors that change the antenna’s electrical length to cover different bands.
• Characteristic mode analysis: Identify and excite multiple chassis modes that radiate at different frequencies.

Modern smartphones often use a combination of these techniques to cover 600MHz–6GHz with 2–4 antenna apertures.

SAR (Specific Absorption Rate) measures the rate of RF energy absorption by the human body, in W/kg. Regulatory limits are typically 1.6 W/kg (FCC, 1g average) or 2.0 W/kg (ICNIRP, 10g average).

Antenna design affects SAR through:

• Antenna placement: Moving the antenna away from the user’s head/body reduces SAR.
• Current distribution: Distributing currents over a larger area reduces peak SAR.
• Ground plane design: Proper ground plane currents can redirect radiation away from the body.
• Power control: Reducing transmit power near the body (proximity sensors).

De-sense (desensitization) is degradation of receiver sensitivity caused by noise or interference from co-located transmitters or digital circuits coupling into the receive antenna.

Causes:

• Harmonics or broadband noise from nearby TX falling into the RX band.
• Digital clock harmonics or switching regulator spurs coupling to the antenna.
• Poor isolation between TX and RX antenna ports.

Mitigation: Improve antenna-to-antenna isolation (spacing, orthogonal polarization, placement), add filtering at the TX output and RX input, shield noise sources, improve PCB layout to reduce coupling, and use notch filters for known interferers.

This is a trick question. In the Friis equation, the (λ/4πd)² term becomes greater than 1 when d < λ/4π. However, the Friis equation is a far-field approximation and is not valid at such short distances. In the near field, energy coupling is governed by reactive near-field mechanisms, not free-space propagation. Conservation of energy tells us you can't create power from nothing.

An isotropic antenna — a theoretical point source that radiates equally in all directions. It has directivity = 1 (0dBi) and serves as the reference for antenna gain measurements. No physical antenna is truly isotropic, but it is the fundamental reference for dBi (decibels relative to isotropic).

The intrinsic impedance of free space is:

It represents the ratio of E-field to H-field magnitudes in a plane wave propagating through free space (η₀ = |E|/|H|). This is a fundamental physical constant that arises from the permittivity and permeability of vacuum. It’s the characteristic impedance that a wave “sees” when propagating through empty space, analogous to a transmission line’s Z₀.